A physical quantity sensor represented by an oscillation type angular velocity sensor generally needs a detector circuit for detecting an output signal from a sensor element thereof and extracting a signal component therefrom. As one of such detector circuits, there is known a detector circuit that uses a Gilbert multiplier being an analog multiplier circuit (for example, Patent Literature 1).
The Gilbert multiplier (Gilbert multiplier core) generally includes a dual differential circuit formed of four bipolar transistors, and outputs a signal proportional to a product of two input signals. The Gilbert multiplier that uses the bipolar transistors has a problem of nonlinearity caused by exponential characteristics of the bipolar transistors. Therefore, there is also known an analog multiplier circuit provided with a circuit that performs preprocessing for achieving linearization by suppressing nonlinear components in the Gilbert multiplier core (for example, Non Patent Literature 1).
An example of such a conventional analog multiplier circuit that uses the Gilbert multiplier core is described with reference to FIG. 9. The analog multiplier circuit 100 includes a Gilbert multiplier core 101 and a linearizer circuit 102.
The Gilbert multiplier core 101 includes a dual differential circuit formed of four bipolar transistors including a pair of bipolar transistors Q1 and Q2 and a pair of bipolar transistors Q3 and Q4. The Gilbert multiplier core 101 outputs an output signal based on a differential current proportional to the product of a first input signal, which is input to a first input terminal pair including Ta and Tb each being a common emitter node of the pair of transistors, and a second input signal, which is input to a second input terminal pair including Tc and Td each being a common base node, from an output terminal pair including Te and Tf each being a common collector node.
The linearizer circuit 102 is an I-V conversion circuit that performs preprocessing for achieving linearization by using an arc hyperbolic function (tan h−1) to suppress the nonlinear components caused by the exponential characteristics of the bipolar transistors Q1 to Q4 that form the Gilbert multiplier core 101. The linearizer circuit 102 includes a pair of bipolar transistors Q5 and Q6 being linearizing transistors connected between the respective terminals of the second input terminal pair Tc and Td of the Gilbert multiplier core 101 and a negative power source (−V). Each of the bipolar transistors Q5 and Q6 is diode-connected, that is, has its base and its collector directly connected to each other. The diode-connected bipolar transistors Q5 and Q6 are each connected in a forward direction along a direction in which a current flows.
When the product of two input signals Vy and Vx each being a voltage signal is obtained by the analog multiplier circuit 100, the input signal Vy is converted by a V-I conversion circuit 110 into a differential current including positive and negative current signals (+K1·Vy) and (−K1·Vy) by using a conversion factor K1. The differential current has a bias current I0 added to each of its components by constant current sources 2a and 2b to be set as a differential current (I0±K1·Vy) including the bias current, which is input to the second input terminal pair Tc and Td of the Gilbert multiplier core 101. On this occasion, the differential current (I0±K1·Vy) is converted into a differential voltage signal Vi expressed by the following expression by the linearizer circuit 102, and input to the Gilbert multiplier core 101. VT is a so-called thermal voltage.Vi=2·VT·tan h−1(K1·Vy/I0)
On the other hand, the input signal Vx is converted by a V-I conversion circuit 120 into a differential current having positive and negative current signals (+K2·Vx) and (−K2·Vx) by using a conversion factor K2. The differential current has a bias current Ib added to each of its components by constant current sources 2c and 2d to be set as a differential current (Ib±K2·Vx) including the bias current, which is input to the first input terminal pair Ta and Tb of the Gilbert multiplier core 101.
With this configuration, a differential current I4 (a pair of positive and negative currents) is output as a multiplication result from the output terminal pair Te and Tf of the Gilbert multiplier core 101. An I-V conversion circuit 150 converts the differential current I4 into a voltage by using a conversion factor K5, and outputs an output voltage Vout expressed by the following expression.Vout=2·K1·K2·K5·(Vx·Vy/I0)
The coefficient “2” on the right-hand side of the above-mentioned expression is a factor corresponding to the fact that the voltage doubles due to the respective conversion of the positive and negative components. By indicating the factor “2” and the conversion factors K1, K2, and K5 collectively by K, the above-mentioned expression can be rewritten as follows. Note that, the bias current Ib is canceled, and therefore does not appear in the final expression of Vout.Vout=K·(Vx·Vy/I0)
I0 is the bias current from the constant current source, and hence the output voltage Vout is proportional to the product Vx·Vy of the two input signals. When a setting is made so that K/I0=1, Vout=Vx−Vy is derived. In this manner, the product of the two input signals can be obtained.